#### Submissions from 2015

ALGEBRAIC AND NUMERICAL EXPLORATION OF FREE ENERGIES FOR MATERIALS WITH MEMORY, Murrough Golden, Giovambattista Amendola, and Mauro Fabrizio

Derivatives Pricing with Accelerated Trinomial Trees, Conall O'Sullivan and Stephen O'Sullivan

A Class of High-Order Runge-Kutta-Chebyshev Stability Polynomials, Stephen O'Sullivan

On Mikhailov's Reduction Group, Tihomir I. Valchev

#### Submissions from 2014

Free Energies in a General Non-Local Theory of a Material with Memory, Giovambattista Amendola, Mauro Fabrizio, and Murrough Golden

Hamiltonian Approach to the Modeling of Internal Geophysical Waves with Vorticity, Alan Compelli

Hamiltonian Formulation of 2 Bounded Immiscible Media with Constant Non-Zero Vorticities and a Common Interface, Alan Compelli

SYMMETRY AND REDUCTIONS OF INTEGRABLE DYNAMICAL SYSTEMS: PEAKON AND THE TODA CHAIN SYSTEMS, Vladimir Gerdjikov, Rossen Ivanov, and Gaetano Vilasi

Free Energies for Materials with Memory in Terms of State Functionals, Murrough Golden

One-Dimensional Weakly Nonlinear Model Equations for Rossby Waves, David Henry and Rossen Ivanov

Matrix G-strands, Darryl Holm and Rossen Ivanov

A Linearised Singularly Perturbed Convection-Diffusion Problem with an Interior Layer, Eugene O'Riordan and Jason Quinn

A Numerical Method for a Nonlinear Singularly Perturbed Interior Layer Problem Using an Approximate Layer Location, Jason Quinn

Dressing Method and Quadratic Bundles Related to Symmetric spaces: Vanishing Boundary Conditions, Tihomir I. Valchev

#### Submissions from 2013

Mathematical Modelling at Secondary School: the MACSI-Clongowes Wood College Experience, J.P.F. Charpin, S. O'Hara, and D. Mackey

Eigenfunction Expansions Associated with the One-Dimensional Schrödinger Operator, Daphne Gilbert

Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators II, Daphne Gilbert, B. J. Harris, and S. M. Riehl

On the Persistence Properties of the Cross-Coupled Camassa-Holm System, David Henry, Darryl Holm, and Rossen Ivanov

G-Strands and Peakon Collisions on Diff(R), Darryl Holm and Rossen Ivanov

Particle Trajectories in Extreme Stokes Waves Over Inifinte Depth, Tony Lyons

Mass Transfer from a Vertical Flat Plate due to a Constant Upward Flow, David McDonnell, Brendan Redmond, and Lawrence J. Crane

Mass Transfer from a Vertical Flat Plate due to Natural Convection with a Constant Counterflow, David McDonnell, Brendan Redmond, and Lawrence J. Crane

Pricing European And American Options In The Heston Model With Accelerated Explicit Finite Differencing Methods, Conall O'Sullivan and Stephen O'Sullivan

Weyl-Titchmarsh Type Formula for Periodic Schrodinger Operator with Wigner-von Neumann Potential, Sergey Simonov and Pavel Kurasov

Spectral multiplicity of selfadjoint Schrodinger operators on star-graphs with standard interface conditions, Sergey Simonov and Harald Woracek

On the Quadratic Bundles Related to Hermitian Symmetric Spaces, Tihomir Ilchev Valchev

Holomorphic Basis for Families of Subspaces of a Banach Space, Milena Venkova and Christopher Boyd

#### Submissions from 2012

Second Gradient Viscoelastic Fluids: Dissipation Principle and Free Energies, G. Amendola, M. Fabrizio, and Murrough Golden

Existence of a Minimizer for the Quasi-Relativistic Kohn-Sham Model, Carlos Argáez García and Michael Melgaard

Hadamard Renormalisation of the Stress Energy Tensor on the Horizons of a Spherically Symmetric Black Hole Space-Time, Cormac Breen and Adrian Ottewill

Hadamard Renormalization of the Stress Energy Tensor in a Spherically Symmetric Black Hole Space-Time with an Application to Lukewarm Black Holes, Cormac Breen and Adrian Ottewill

Stiefel and Grassmann Manifolds in Quantum Chemistry, Eduardo Chiumiento and Michael Melgaard

On Soliton Interactions for a Hierarchy of Generalized Heisenberg Ferromagnetic Models on SU(3)/S(U(1) $\times$ U(2)) Symmetric Space, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, and Tihomir VAlchev

On Projection-Invariant Subgroups of Abelian P-Groups, Brendan Goldsmith

On Maximal Relatively Divisible Submodules, Brendan Goldsmith and Paolo Zanardo

The Generalised Zakharov-Shabat System and the Gauge Group Action, Georgi Grahovski

G-Strands, Darryl Holm, Rossen Ivanov, and James Percival

Dark Solitons of the Qiao's Hierarchy, Rossen Ivanov and Tony Lyons

Integrable Models for Shallow Water With Energy Dependent Spectral Problems, Rossen Ivanov and Tony Lyons

Cyclic Universe with an Inflationary Phase from a Cosmological Model with Real Gas Quintessence, Rossen Ivanov and Emil Prodanov

The 2-Component Dispersionless Burger's Equation Arising In The Modelling Of Bloodflow, Tony Lyons

Multiple Solutions of the Quasi Relativistic Choquard Equation, Michael Melgaard and Frederic D. Y. Zongo

#### Submissions from 2011

Solutions to quasi-relativistic multi-configurative Hartree-Fock equations in quantum chemistry, Carlos Argáez García and Michael Melgaard

Holomorphic Liftings from Infinite Dimensional Spaces, Sean Dineen and Milena Venkova

Multifluid Magnetohydrodynamic Turbulent Decay, Turlough Downes and Stephen O'Sullivan

Euler Equations on a Semi-Direct Product of the Diffeomorphisms Group by Itself, Joachim Escher, Rossen Ivanov, and Boris Kolev

On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources, Vladimir Gerdjikov, Georgi Grahovski, and Rossen Ivanov

Rational Bundles and Recursion Operators for Integrable Equations on A.III-type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander Mikhailov, and Tihomir Valtchev

Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces, Vladimir Gerdjikov, Georgi Grahovski, Alexander V. Mikhailov, and Tihomir Valchev

On the N-Wave Equations and Soliton Interactions in Two and Three Dimensions, Vladimir S. Gerdjikov, Rossen Ivanov, and Assen V. Kyuldjiev

On socle-regularity and some notions of transitivity for Abelian p-groups, Brendan Goldsmith and Peter Danchev

On Adjoint Entropy of Abelian Groups, Brendan Goldsmith and Ketao Gong

A Stability Study of a New Explicit Numerical Scheme for a System of Differential Equations with a Large Skew-Symmetric Component, Katharine Gurski and Stephen O'Sullivan

Smooth and Peaked Solitons of the Camassa-Holm Equation and Applications, Darryl Holm and Rossen Ivanov

On the Acceleration of Explicit Finite Difference Methods for Option Pricing, Stephen O'Sullivan and Conall O'Sullivan

#### Submissions from 2010

Spectral Theory of Semibounded Sturm-Liouville Operators with Local Interactions on a Discrete Set, Sergio Albeverio, Aleksey Kostenko, and Mark Malamud

Study of the Photoinduced Surface Relief Modulation in Photopolymers caused by Illumination with a Gaussian Beam of Light, Tzvetanka Babeva, Dana Mackey, Suzanne Martin, Izabela Naydenova, and Vincent Toal

Two-way Diffusion Model for Short Exposure Holographic Grating Formation in Acrylamide-based Photopolymer, Tzvetanka Babeva, Izabela Naydenova, Dana Mackey, Suzanne Martin, and Vincent Toal

Extended Green-Liouville asymptotics and vacuum polarization for lukewarm black holes, Cormac Breen and Adrian Ottewill

Inverse scattering transform for the Degasperis–Procesi equation, Adrian Constantin, Rossen Ivanov, and Jonatan Lenells

Multi–component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory, Vladimir Gerdjikov and Georgi Grahovski

On the socles of characteristic subgroups of Abelian p-groups, Brendan Goldsmith and Peter Danchev

The maximal pure spectrum of an Abelian group, Brendan Goldsmith and Ruediger Goebel

Schrödinger Operators with δ'Interactions and the Krein–Stieltjes String, Aleksey Kostenko and M. M. Malamud

Complex absorbing potential method for systems, Jimmy Kungsman and Michael Melgaard

A Diffusion Model for Spatially Dependent Photopolymerization, Dana Mackey, Tzvetanka Babeva, Izabela Naydenova, and VIncent Toal

Heat Transfer through the Boundary Layer on a Moving Cylindrical Fibre, Brendan Redmond and David McDonnell

A Model for Predicting Extragalactic Jet Lifetimes, Daniel S. Spicer, Robert Bingham, and Stephen O'Sullivan

From Permutahedron to Aassociahedron, Colum Watt and Thomas Brady

From Permutahedron to Associahedron, Colum Watt and Thomas Brady

Climbing Eements in Finite Coxeter Groups, Colum Watt, Thomas Brady, and Aisling Kenny

#### Submissions from 2009

On the socles of characteristic subgroups of Abelian p-groups, P. V. Danchev and Brendan Goldsmith

Algebraic entropy for Abelian groups, Dikran Dikranjan, Brendan Goldsmith, Luigi Salce, and Paolo Zanardo

Nonideal Magnetohydrodynamic Turbulent Decay in Molecular Clouds, Turlough Downes and Stephen O'Sullivan

Existence of infinitely many distinct solutions to the quasi-relativistic Hartree-Fock equations, Mattias Enstedt and Michael Melgaard

On modules which are self-slender, R. Gobel, Brendan Goldsmith, and O. Kolman

Phase Transitions in Materials with Thermal Memory: the Case of Unequal Conductivities, Murrough Golden

On the socles of fully invariant Abelian p-groups, Brendan Goldsmith and P. V. Danchev

Generalised Fourier Transform and Perturbations to Soliton Equations, Georgi Grahovski and Rossen Ivanov

Converging Flow Between Coaxial Cones, O. Hall, A. D. Gilbert, and C. P. Hills

Nonaxisymmetric Stokes Flow Between Concentric Cones, O. Hall, C. P. Hills, and A. D. Gilbert

Equations of the Camassa-Holm Hierarchy, Rossen Ivanov

Two component integrable systems modelling shallow water waves: the constant vorticity case, Rossen Ivanov

An Analysis of Drug Dissolution Rates in the USP 24 Type 2 Apparatus, David McDonnell, Brendan Redmond, Deirdre M. D'Arcy, Anne Marie Healy, and Owen Corrigan

Stochastic particle acceleration in the lobes of giant radio galaxies, Stephen O'Sullivan, Brian Reville, and Andrew Taylor

Daemon Decay and Inflation, Emil Prodanov

#### Submissions from 2008

On an integrable two-component Camassa-Holm shallow water system, Adrian Constantin and Rossen Ivanov

Nearly-Hamiltonian Structure for Water Waves with constant vorticity, Adrian Constantin, Rossen Ivanov, and Emil Prodanov

Existence of a solution to Hartree-Fock equations with decreasing magnetic field, Mattias Enstedt and Michael Melgaard

Higher derivatives of spectral functions associated with one-dimensional schrodinger operators, Daphne Gilbert, B.J. Harris, and S.M. Riehl

Algebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations, Rossen Ivanov

Non-existence of a minimizer to the Hartree-Fock functional, Michael Melgaard and Mattias Enstedt

Interacting Jets From Binary Protostars, Gareth Murphy, Thibaut Lery, Stephen O'Sullivan, Daniel S. Spicer, Francesca Bacciotti, and Alex Rosen

Equation of State for a van der Waals Universe during Reissner–Nordstrom Expansion, Emil Prodanov, Rossen Ivanov, and Vesselin Gueorguiev

Environmental limits on the nonresonant cosmic-ray current-driven instability, Brian Reville, John Kirk, Peter Duffy, and Stephen O'Sullivan

The transport of Cosmic Rays in Self‐Excited Magnetic Turbulence, Brian Reville, Stephen O'Sullivan, Peter Duffy, and John Kirk

Non-crossing Partition Lattices in Finite Real Reflection Groups, Colum Watt and Thomas Brady

#### Submissions from 2007

Hamiltonian formulation, nonintegrability and local bifurcations for the Ostrovsky equation, S. Roy Choudhury, Rossen Ivanov, and Yue Liu

Krylov subspaces from bilinear representations of nonlinear systems, Marissa Condon and Rossen Ivanov

Generalised Fourier transform for the Camassa-Holm hierarchy, Adrian Constantin, Vladimir Gerdjikov, and Rossen Ivanov